| Min(phi) over symmetries of the knot is: [-3,-1,0,2,2,0,1,2,4,0,0,1,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['5.46'] |
| Arrow polynomial of the knot is: -4*K1**3 + 4*K1**2 + 2*K1*K2 + 2*K1 - 2*K2 - 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['5.37', '5.46', '7.4212', '7.4216', '7.5182', '7.6010', '7.6740', '7.8735', '7.8895', '7.8903', '7.10036', '7.10817', '7.10909', '7.11122', '7.11714', '7.11850', '7.11971', '7.12386', '7.12483', '7.12745', '7.12845', '7.12926', '7.13747', '7.14086', '7.14088', '7.15063', '7.15499', '7.15524', '7.15675', '7.16458', '7.17003', '7.17142', '7.17157', '7.17172', '7.17210', '7.17376', '7.18076', '7.18186', '7.18257', '7.18299', '7.18418', '7.18445', '7.18463', '7.18726', '7.18732', '7.18804', '7.18898', '7.18997', '7.19685', '7.20499', '7.20505', '7.20597', '7.20603', '7.20637', '7.20854', '7.20896', '7.20904', '7.20995', '7.21048', '7.21086', '7.21274', '7.21326', '7.21393', '7.21424', '7.21571', '7.21603', '7.21623', '7.21748', '7.21818', '7.21893', '7.22041', '7.22081', '7.22239', '7.22256', '7.22312', '7.22404', '7.22491', '7.23028', '7.23120', '7.23140', '7.23166', '7.23708', '7.23723', '7.23959', '7.24142', '7.24238', '7.24284', '7.25142', '7.27724', '7.31432', '7.31528', '7.31554', '7.31605', '7.31648', '7.31660', '7.31691', '7.31716', '7.31775', '7.31789', '7.31850', '7.31926', '7.31985', '7.32012', '7.32022', '7.32025', '7.32087', '7.32092', '7.32098', '7.32138', '7.32155', '7.32169', '7.32855', '7.33089', '7.33090', '7.33091', '7.33117', '7.33142', '7.33202', '7.33247', '7.33322', '7.33352', '7.33425', '7.33464', '7.33996'] |
| Outer characteristic polynomial of the knot is: t^6+43t^4+19t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.46'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 - 192*K1**2*K2**4 + 352*K1**2*K2**3 - 704*K1**2*K2**2 + 680*K1**2*K2 - 16*K1**2*K3**2 - 620*K1**2 + 160*K1*K2**3*K3 + 496*K1*K2*K3 + 48*K1*K3*K4 + 16*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 224*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 64*K2**2*K4 - 200*K2**2 + 8*K2*K3*K5 - 156*K3**2 - 44*K4**2 - 8*K5**2 + 410 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.46'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.167', 'vk5.206', 'vk5.301', 'vk5.356', 'vk5.652', 'vk5.799', 'vk5.1171', 'vk5.1314', 'vk5.1380', 'vk5.1401', 'vk5.1416', 'vk5.1441', 'vk5.1661', 'vk5.1783', 'vk5.1883', 'vk5.1943'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3O4U2U3O5U1U5U4 |
| R3 orbit | {'O1O2O3O4U2U3O5U1U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U4O5U2U3 |
| Gauss code of K* | O1O2O3U1U4U5U3O4O5U2 |
| Gauss code of -K* | O1O2O3U2O4O5U1U4U5U3 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -2 0 3 1],[ 2 0 -1 1 4 1],[ 2 1 0 1 2 0],[ 0 -1 -1 0 1 0],[-3 -4 -2 -1 0 0],[-1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 0 -2 -2],[-3 0 0 -1 -2 -4],[-1 0 0 0 0 -1],[ 0 1 0 0 -1 -1],[ 2 2 0 1 0 1],[ 2 4 1 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,2,2,0,1,2,4,0,0,1,1,1,-1] |
| Phi over symmetry | [-3,-1,0,2,2,0,1,2,4,0,0,1,1,1,-1] |
| Phi of -K | [-2,-2,0,1,3,-1,1,3,3,1,2,1,1,2,2] |
| Phi of K* | [-3,-1,0,2,2,2,2,1,3,1,2,3,1,1,-1] |
| Phi of -K* | [-2,-2,0,1,3,-1,1,1,4,1,0,2,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+2t^2-t |
| Normalized Jones-Krushkal polynomial | -5z-9 |
| Enhanced Jones-Krushkal polynomial | 4w^3z-9w^2z-9w |
| Inner characteristic polynomial | t^5+25t^3+7t |
| Outer characteristic polynomial | t^6+43t^4+19t^2 |
| Flat arrow polynomial | -4*K1**3 + 4*K1**2 + 2*K1*K2 + 2*K1 - 2*K2 - 1 |
| 2-strand cable arrow polynomial | -16*K1**4 - 192*K1**2*K2**4 + 352*K1**2*K2**3 - 704*K1**2*K2**2 + 680*K1**2*K2 - 16*K1**2*K3**2 - 620*K1**2 + 160*K1*K2**3*K3 + 496*K1*K2*K3 + 48*K1*K3*K4 + 16*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 224*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 64*K2**2*K4 - 200*K2**2 + 8*K2*K3*K5 - 156*K3**2 - 44*K4**2 - 8*K5**2 + 410 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 5}, {1, 4}, {2}], [{4, 5}, {1, 3}, {2}]] |
| If K is slice | False |